Divide the polynomials.
Usually, there are many different ways to divide polynomials. Here, we will use the method of splitting the quotient into multiple quotients: $\dfrac{4x^3-x^2+3}{x}=\dfrac{4x^3}{x}-\dfrac{x^2}{x}+\dfrac{3}{x}$ Now let's try to cancel common factors in the resulting terms. $\begin{aligned} \dfrac{4x^3}{x}&=4x^2 \\\\ -\dfrac{x^2}{x}&=-x \end{aligned}$ $\dfrac{3}{x}$ doesn't have common factors so it has to stay as it is. In conclusion, this is the result of dividing the polynomials: $4x^2-x+\dfrac{3}{x}$ [I want to see a different way of performing the division.]